Thermal partition function of $J_3 \bar{J}_3$ deformed $AdS_3$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913306767261696 |
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| author | Chakraborty, Soumangsu Giveon, Amit Hashimoto, Akikazu |
| author_facet | Chakraborty, Soumangsu Giveon, Amit Hashimoto, Akikazu |
| contents | We derive a compact formula for the one-loop, bosonic string partition function of Euclideanized $J_3 \bar J_3$ deformed $AdS_3$ with periodic Euclidean time as an integral transform of the partition function of the undeformed Euclideanized $AdS_3$. Such a deformation is interpretable as an irrelevant "single-trace $T \bar T$ deformation" of the boundary. We will do this by first establishing a formal procedure to compute a worldsheet torus zero point function for an exactly marginal $J \bar J$ deformation of a sigma model with $U(1)_L \times U(1)_R$ global symmetry. We then describe how this procedure is implemented on $SL(2,R)$ sigma model and its Euclidean continuation. Finally, we describe the embedding of the deformed $SL(2,R)$ torus amplitude into critical string theory and interpret the result as the leading perturbative contribution to the thermal partition function of the deformed theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03979 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Thermal partition function of $J_3 \bar{J}_3$ deformed $AdS_3$ Chakraborty, Soumangsu Giveon, Amit Hashimoto, Akikazu High Energy Physics - Theory We derive a compact formula for the one-loop, bosonic string partition function of Euclideanized $J_3 \bar J_3$ deformed $AdS_3$ with periodic Euclidean time as an integral transform of the partition function of the undeformed Euclideanized $AdS_3$. Such a deformation is interpretable as an irrelevant "single-trace $T \bar T$ deformation" of the boundary. We will do this by first establishing a formal procedure to compute a worldsheet torus zero point function for an exactly marginal $J \bar J$ deformation of a sigma model with $U(1)_L \times U(1)_R$ global symmetry. We then describe how this procedure is implemented on $SL(2,R)$ sigma model and its Euclidean continuation. Finally, we describe the embedding of the deformed $SL(2,R)$ torus amplitude into critical string theory and interpret the result as the leading perturbative contribution to the thermal partition function of the deformed theory. |
| title | Thermal partition function of $J_3 \bar{J}_3$ deformed $AdS_3$ |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2403.03979 |